Let $N(m,n)$ denote the number of partitions of $n$ with rank $m$. In 2014, Chan and Mao proved that $N(m,n)geq N(m+2,n)$ for all $mgeq 0$, and for $ngeq 10,$ $N(m,n)geq N(m,n-1)$. In this talk, we will generalize their results to crank and overpartitions. We also recall the definition of spt-function and spt-crank, and show that the spt-crank is unimodal and define it on marked partitions. This work is joint work with Kathy Ji, Huan Xiong and Helen Zhang.